Heat olive oil in a large nonstick sauté pan over medium-high and add kielbasa. Cook, without stirring for 1 minute. Then stir occasionally for about 3 minutes. Transfer to a plate with a slotted spoon.

In the same pan with some of the rendered kielbasa fat, add the cabbage, onion, garlic, sugar, salt, and pepper. Stir to combine and cook for about 10 minutes, stirring occasionally.

Mix in the vinegar and mustard; add the sausage back to the pan and cook for another 2 minutes to heat through. Taste and adjust seasoning, if necessary.